Comparison between Kirchhoff index and the Laplacian-energy-like invariant

Abstract: Let G be a connected graph of order n with Laplacian eigenvalues . The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as and , respectively. We compare Kf and LEL and establish two sufficient conditions under which . The connected graphs of order n with nine greatest Kirchhoff indices are determined; for these holds. [Copyright &y& Elsevier]